An automatic grinding machine in an auto parts plant prepares axles with a target diameter μ = 40.15 millimeters (mm). The machine has some variability, so the standard deviation of the diameters is σ = 0.02 mm. A sample of 9 axles is inspected each hour for process control purposes, and records are kept of the sample mean diameter. If the process mean is exactly equal to the target value, what will be the mean and standard deviation of the numbers recorded?
μx =
σx =
Averages are less variable than individual observations. Suppose that the axle diameters vary according to a normal distribution. In that case, the mean x of an SRS of axles also has a normal distribution. What is the probability that the diameter of a single randomly chosen axle differs from the target value by 0.01 mm or more (in either direction)?
What is the probability that the mean diameter of an SRS of 9 axles differs from the target value by 0.01 mm or more (in either direction)?